Some results for repairable systems with general repair

This paper develops general repair models for a repairable system by using the idea of the virtual age process of the system. If the system has the virtual age immediately after the th repair, the nth failure-time is assumed to have the survival function where is the survival function of the failure-time of a new system. A general repair is represented as a sequence of random variables taking a value between 0 and 1, where denotes the degree of the nth repair. For the extremal values 0 and 1, means a minimal repair and a perfect repair. Two models are constructed depending on how the repair affects the virtual age process: as Model 1 and as Model II. Various monotonicity properties of the process with respect to stochastic orderings of general repairs are obtained. Using a result, an upper bound for when a general repair is used is derived.